The partial K function

• 成果类型: Article; Early Access
• 署名作者: Grainger, Jake P.; Rajala, Tuomas A.; Murrell, David J.; Olhede, Sofia C.
• 署名单位: Natural Resources Institute Finland (Luke); University of London; University College London
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag123
• 发表日期: 2026-09-10
• 关键词: multivariate point processes; Partial Correlation; partial K function; point pattern analysis; Ripley's K function; spatial point processes

摘要

The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or between two different types of points. In this paper, we introduce a partial K function, enabling us to account for some of the effects of the other point types when analysing point-point interactions. The partial K function we introduce reduces to the usual K function when the other points are independent of the points of interest and has a similar interpretation. Using examples, we demonstrate how the partial K function can unpick dependence between point types that would otherwise be hidden in the usual K function. We also discuss important bias correction steps and hyperparameter selection. In addition, we introduce an extension to account for other spatial covariates, and demonstrate the methodology on the Lansing Woods dataset.